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Pear Curve

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PearCurve

For some range of r, the Mandelbrot set lemniscate L_3 in the iteration towards the Mandelbrot set is a pear-shaped curve. In Cartesian coordinates with a constant r, the equation is given by

r^2=(x^2+y^2)(1+2x+5x^2+6x^3+6x^4+4x^5+x^6-3y^2-2xy^2+8x^2y^2+8x^3y^2+3x^4y^2+2y^4+4xy^4+3x^2y^4+y^6).

The plots above show the resulting curve for r=2 (left figure) and for a range of r between 0 and 2 (right figure).

See also

Mandelbrot Set, Mandelbrot Set Lemniscate, Pear-Shaped Curve, Piriform Curve, Teardrop Curve

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Cite this as:

Weisstein, Eric W. "Pear Curve." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PearCurve.html

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